Based on the position equation of 3-PUU parallel mechanism, the influence coefficient matrix of 3-PUU parallel mechanism was established by using dummy mechanism method, including Jacobian matrix and Hessian matrix. The mapping relation of the velocity and acceleration of the drive mechanism and the moving platform of the parallel mechanism were obtained by using the influence coefficient matrix and the differential equation of the position equation.The velocity and acceleration of the drive mechanism solved through the influence coefficient matrix and the differential equation were compared with the ADAMS simulation results.The consistency of the three analytical methods verify the correctness of the kinematics theory analysis, the reliability of the simulation verification, and usability of the 3-PUU parallel mechanism as the main body of the laser cutting machine tool.It provides reference for the dynamic analysis of the mechanism, the establishment of the performance index and the optimization design